> Seems clear enough: in ZFC, there are uncountably many irrationals,> each of which is an endpoint of a closed interval with zero. And,> they nest. Yet, there aren't uncountably many nested intervals, as> each would contain a rational.

While there is no SEQUENCE of uncountably may nested intervals, which the very definition of sequence prohibits, there are certainly SETS of uncountably many nested intervals.

EXAMPLE: For each real x in (0,1), [x, 2-x] is closed real interval and the set of such intervals is both nested and uncountable. But it is not a SEQUENCE of intervals.

So that what Ross thought was a paradox is just a kink in his thinker.--